Question

Philip ran out of time while taking a multiple-choice test and plans to guess the last 4 questions. Each question has 5 possible choices, one of which is correct. Let X=X=X, equal the number of answers Philip correctly guesses in the last 444 questions. Assume that the results of his guesses are independent.
What is the probability that he answers exactly 1 question correctly in the last 4 questions?

Answer 1

Using the binomial distribution, it is found that there is a 0.4096 = 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.

What is the binomial distribution formula?

The formula is:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

• x is the number of successes.

• n is the number of trials.

• p is the probability of a success on a single trial.

Considering that there are 4 questions, and each has 5 choices, the parameters are given as follows:

n = 4, p = 1/5 = 0.2.

The probability that he answers exactly 1 question correctly in the last 4 questions is P(X = 1), hence:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 1) = C_{4,1}.(0.2)^{1}.(0.8)^{3} = 0.4096$

0.4096 = 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.

More can be learned about the binomial distribution at brainly.com/question/24863377

#SPJ1